There’s a certain strain of modern American plays in which family members dedicate themselves to saying the most outrageous things to one another, in an implacable effort to slit each other’s throats with wit.

Not that Baitz’s story of a family riven by politics and a tragic past should be judged solely on its level of biting humor. But at least as staged in an absorbing but tonally bumpy production at the Old Globe, the play does lean hard on the laugh lines, especially in the first act. (On opening night, boisterous audience reaction drowned out follow-up dialogue at several points.)

And while Baitz does weave in some good zingers, at times those lines try a bit too hard to be wry: “He’s too old and too British — which is the same thing, really” (said of one character’s husband) is one that feels a few degrees away from landing.

It’s part of a larger issue with the play, at least to these ears (and I fully recognize I’m in the minority on “Desert Cities,” which was a Pulitzer finalist in 2012 and had a healthy Broadway run). While director Richard Seer’s cast brings a sharp sense of nerves chafed raw by decades of loved ones’ reflexive aggression, the way these characters relate can feel tinged by inauthenticity for the sake of the comic. That sense is heightened by a tendency for the story to strain under the weight of exposition stacked onto what’s meant to be normal conversation.

Of course, give Baitz this: There’s a lot for an audience to catch up on, because the Wyeth family is all about back story.

The action begins at Christmas 2004, as young-adult siblings Brooke (Dana Green) and Trip (Andy Bean) visit the expansive Palm Springs home of their parents, Lyman (Robert Foxworth) and Polly (Kandis Chappell). (Alexander Dodge has designed those digs to spectacular, midcentury-modern perfection, but the living room alone is so vast that the actors can seem lost in it.)

The parents are both long-ago Hollywood veterans turned conservative political heavyweights; the kids are diehard liberals who likewise work in entertainment, of a fashion. Trip produces a TV show that sounds like a lower-brow version of “The People’s Court.” Of more import to the story — in fact, it’s the catalyst for looming catastrophe — Brooke is a writer, and her latest book is a Wyeth tell-all.

The memoir focuses mostly on the fate of her older brother, Henry, who devoted himself to radical causes in the 1970s, was implicated in a deadly bombing and eventually leaped from a ferry into oblivion. Brooke, who was close to Henry, has struggled to move on, losing years to depression.

“I want to talk about Henry until it makes sense,” she tells her family.

But the parents aren’t having it. Tough and emotionally Teflon’d Polly, played by Chappell (who seems in the midst of a dazzling career renaissance) with a masterful sense of the imperious, objects the most forcefully at first. But the bottled-up Lyman — whom the versatile Foxworth lends a laconic sense of resignation and dry humor — finally boils over, too.

Green plumbs Brooke’s depths of despair (and flinty exterior) with sensitivity and insight (and works up volcanic passions toward the end). And while Trip sometimes seems there more as sounding board than fleshed-out character, Bean gives him an oddball, what-the-hell wit.

And then there’s Silda, Polly’s sister, a lifelong leftie (and drinker) who’s barely hanging onto the wagon. Robin Pearson Rose lends her a matchless comic touch and gets some of the show’s best laughs.

“Other Desert Cities” (named for a phrase on a freeway sign) takes its time reaching an 11th-hour twist. But there are moments in the tense second act that weave together nicely all the threads of politics, truth-telling and family legacy. (The production also boasts polished contributions from York Kennedy’s desert-umber lighting, Paul Peterson’s spacious sound and Charlotte Devaux’s spot-on costumes — especially her sleek tennis warmups for Lyman and Polly.)

In one moment that’s both startling and weirdly touching, Polly leans in and plants a kind of Judas smooch on Brooke. It’s a kiss that seems more like a fist.